The development of models for the prediction of combustion in supersonic flows must take into account the specific features of these flows, in which couplings exist between compressibility, mixing, and exothermic chemistry. Indeed, it has been shown in our previous work that, in the case of laminar boundary and mixing layers, viscous dissipation heating plays an essential role in the development of the chemical process and thus on the resulting structure of combustion. This phenomenon, which is connected to the conversion of kinetic energy to enthalpy, must be included in any model intended to describe combustion in supersonic flows. Moreover, such models must also bear a correct description of the interaction between the instantaneous velocity field and mixing, as well as a correct description of the gas dynamical compressibility. In the present work a model is presented, which includes an extension to the classical stretched flamelet model based on the conditional moment closure technique, and accounts for the fluctuations of the velocity field.